ELLISVILLE — Mississippi state Sen. Chris McDaniel, the tea party-backed challenger who lost a primary runoff to U.S. Sen. Thad Cochran, has formally asked the state Republican Party to overturn the June 24 election results and declare him the winner.

But McDaniel faces high legal hurdles — with vague evidence — as he extends this midterm election year’s most bitter fight between tea party factions of the conservative movement who backed him and the traditional GOP powers who helped Cochran win by 7,667 votes, a margin of 1.8 percentage points.

McDaniel and his attorney confirmed yesterday that they have filed a formal challenge with the state party, asserting that enough Democratic voters illegally cast runoff ballots to hand the nomination to the six-term incumbent.

“They asked us to put up or shut up, and here we are with the evidence,” McDaniel said in a news conference, as he held up a copy of his appeal based on voter lists from the June 3 primary and the June 24 runoff.

If the state party doesn’t grant McDaniel’s request within 10 days, he can push the matter to state court.

State Republican Chairman Joe Nosef said he needs to review the appeal before commenting.

Mark Garriga, an attorney for Cochran, said in a statement that McDaniel’s challenge “marks the point where this matter moves from an arena of press conferences and rhetoric into a setting where nothing matters but admissible evidence and the rule of law.”

At Republicans’ national Senate campaign office, spokesman Brad Dayspring said, “We’ve been entirely focused on the general election since Senator Cochran’s victory in the runoff.”

Cochran is favored to win a seventh term over Democratic former Congressman Travis Childers and a little-known Reform Party candidate.

McDaniel’s appeal hinges on comparing voter lists from the initial primary, which McDaniel led without winning a majority, and the runoff, when Cochran managed a comeback aided by a sharp increase in turnout in areas with a large number of black voters, a reliably Democratic voting bloc in Mississippi.

Mississippi voters don’t register by party, but state law makes so-called crossover voting — casting a ballot in one party’s primary and then another party’s runoff in the same cycle — a misdemeanor.

Attorney Mitchell Tyner said McDaniel’s campaign had found about 3,500 instances of crossover votes, along with the 9,500 “irregular votes” and 2,275 “improperly cast” absentee ballots. He did not immediately explain what made those votes irregular, or how the absentee ballots may have been improperly cast, saying only that the second pool of ballots “are votes we have questions about.”

The number that dwarfs Cochran’s winning margin, however, is the 40,000 Democrats who McDaniel claims voted in the runoff, a figure that would include explicitly illegal crossover votes, along with self-identifying Democrats who did not vote in the first round.

Cochran made an unapologetic appeal to Democrats and independents during the three-week runoff campaign, and turnout jumped by 63,295 votes to 382,197, with marked increases in majority black counties.

McDaniel has accused Cochran and his backers of “race baiting” and “selling out the conservative movement,” but any legal challenge of that turnout surge hinges on a separate Mississippi election law that courts have declared unenforceable. The law ostensibly bars a voter from casting a primary ballot unless that voter is committed to supporting the party’s nominee in the general election.

Tyner said the McDaniel campaign used statewide polling to identify Democrats who voted in the Republican primary. He claimed that 71 percent of them admitted they wouldn’t back Cochran in November.

Mississippi courts have ordered some new local elections, but there has been no court-ordered do-over of a statewide election in at least the past six decades of records reviewed by The Associated Press. Tyner has said he had found no examples of a Mississippi court ever ordering a new statewide vote.